and I want to run NSolve on a set of equations of this form, for example:

NSolve[{5x + 7y - 6, 9x - 2y + 3}]

How can I use the single definition of eq above to do this, by replacing a, b and c with the required values? It is ok to write it manually in NSolve for a simple example as above, but the real equation I will be doing this with has many more terms, and I will be solving a set of 8 equations!

Overall it'd be great if I could take a single equation like eq above, and then a list of the values that I want to be used (eg. a list of values for a, a list of values for b and a list of values for c) and then generate a list to pass to NSolve.

This is probably a fairly simple question, but I'm a beginner with Mathematica (although an experienced programmer in many other languages), so I'm not sure how to approach it. I suspect there may be a built-in function that will do this (or something like it) - is that the case?

Those lists of values of a and b, when assembled into a list, form a matrix which you can pass directly to LinearSolve along with the list of c values. When you have more equations than variables, though, you need to use a least squares approach: look to LeastSquares and its kin.
–
whuberFeb 5 '13 at 13:17

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